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17 - Sparse Recovery from One-Bit Observations

from Part Three - Compressive Sensing

Published online by Cambridge University Press:  21 April 2022

Simon Foucart
Affiliation:
Texas A & M University
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Summary

This chapter returns to the recovery of sparse vectors, but this time the linear measurements are quantized to retain only their signs. With the help of the restricted isometry property from ?2 to ?1, it is shown that the direction of sparse vectors can still be approximately recovered via a hard thresholding procedure or via a linear program. Furthermore, it is shown that the magnitude, too, can be recovered if an appropriate modification of the signed observations is allowed.

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Publisher: Cambridge University Press
Print publication year: 2022

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